Question

Sa se rezolve sitemul:
$\left \{ {{x+4=4-x} \atop {-2x+y=1+x-y}} \right.$

Answer 1

[tex] \left\{ \begin{array}{c} x+4 = 4-x \\ -2x+y=1+x-y \end{array} \right \Rightarrow\left\{ \begin{array}{c} x+x=4-4 \\ y+y = 1+x+2x \end{array} \right \Rightarrow\\ \\ \Rightarrow \left\{ \begin{array}{c} 2x=0 \\ 2y=1+3x \end{array} \right \Rightarrow \left\{ \begin{array}{c} x=0 \\ 2y=1+3\cdot 0\end{array} \right \Rightarrow \left\{ \begin{array}{c} x=0 \\ 2y=1\end{array} \right \Rightarrow \\ \\ [/tex]

$\Rightarrow \left\{ \begin{array}{c} x=0 \\ y=\dfrac{1}{2}\end{array} \right| \Rightarrow \boxed{(x,y) = \Big(0,\dfrac{1}{2}\Big)}$